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Women have been paid, down the ages, for taking their clothes off in public: now it seems some of them are being asked to pay, and handsomely too, for the privilege of not taking them off.

The row prompted last week by news that Texan actress and former model Amber Heard is being sued for US$10 million ($14m) for reneging on a supposed agreement to be filmed naked has put a compelling new twist on a familiar Hollywood puzzle: why is screen nudity such a big element of so many female stars' early careers? It is a puzzle conventionally posed just after the one about why so many film directors are men.

Last week Billie Piper also spoke out against the continued pressure to appear nude. It was unusual, she told the Evening Standard, to be offered a part without at least one moment of full exposure. She joins stars such as Julia Roberts, Jennifer Garner, Scarlett Johansson and Emma Watson, who have all been careful not to appear nude on screen - either opting for the use of body doubles or for scripts that involve no more than a passionate embrace.

"What's annoying is that they are fun roles if you can remove the sex," Piper said. "It's the sex that makes it annoying. Otherwise they are interesting stories, interesting women with chequered pasts."

The 34-year-old, whose previous roles include not only the family-friendly Rose in the BBC's Doctor Who, but also an escort in the ITV drama Secret Diary Of A Call Girl, is tired of being sent "hooker scripts". Heard's stand was made against a script said to have dictated she appear naked in the new adaptation of Martin Amis's novel London Fields. Her reluctance was reportedly backed up on set by her director, newcomer Matthew Cullen.

Yet Heard's actions appear to have enraged the executives who financed and promoted the thriller at production company Nicola Six Limited. (The company ironically shares the name of Heard's character, the talismanic manipulative sex object of the novel.) London Fields, which also stars her former husband, Johnny Depp, Cara Delevingne and Billy Bob Thornton, was refused an early screening slot at Cannes this summer and has reportedly been heavily re-edited after it left Cullen's hands. The film has no set release date yet, so it is possible that the new legal dispute between Heard and the production company is just one of many ways the thwarted producers intend to try to extract compensation for a potential box office flop.

In response to the lawsuit, some film pundits in America have railed against the idea that nudity should ever be agreed before shooting. The shared artistic vision of the director and his cast will require it, or it will not, critics such as Richard Brody have argued.

Writing in the New Yorker on Friday Brody suggested that it was "repugnant that Heard was put in the position of having to agree to nudity in advance".

He called upon the Screen Actors Guild to "leap in and repudiate even the notion of a nudity rider. There are movies in which an actor's nudity comes about as a result of the artistic process - even when it hasn't been planned in advance, even in the absence of paperwork."

Brody has faith in the possibility of creative integrity. But other commentators see a good case for setting up a contractual agreement that protects anyone from being persuaded to strip on set. It might sound a prim precaution in the bohemian world of entertainment, but in an industry where the casting couch is still a tacitly recognised route to the top, it may have its place. This issue is at the centre of a timely new American film, Always Shine, directed by Sophia Takal, about two young women trying to become film stars.

"One is getting ahead by routinely appearing naked in horror films; the other, who won't undress or play submissive, is stuck with roles in avant-garde independent shorts," explains film critic Jonathan Romney, after reviewing the film for the American journal Film Comment. "The film is a protest against what sometimes seems a hopeless impasse for women in Hollywood."

Romney has a few reservations about the film, as his review makes clear: "The opposition is somewhat schematic, perhaps: vulnerable Beth, who has succeeded by playing the most classically 'feminine' role, versus tough 'masculine' Anna, whose defiantly autonomous nature has damaged her career prospects." But he feels its arguments are germane. The implication of Always Shine is that the film business still makes prostitutes of actresses and unsavoury punters of all who queue up to watch.

Eroticism, in contrast, is a crucial element in many films and is tricky to conjure, no matter how naked the stars. In the case of a classic sex sequence, such as the hotel room scene in Don't Look Now, the intercourse portrayed by stars Donald Sutherland and Julie Christie is as much about cathartic emotion and their recent bereavement as about lust.

The film canon brings plenty of examples of nudity that work, Romney agrees. He points to the work of French director Catherine Breillat, who has shown male and female actors naked in scenes which both emphasise their sexual identity and show them psychologically exposed, and to Isabelle Huppert's nude scene in Claude Goretta's classic of French cinema, The Lacemaker (1977) "as an index of a character's emotional vulnerability".

And several actresses, including Helen Mirren, have managed to glide majestically through quite extraneous sex scenes, rolling, as it were, with the prevailing mood of the age. In the later stages of her career she has been hailed again as a great actress, sustaining no obvious damage from all the saucy quips once levelled at her. Equally the British Oscar-nominee Carey Mulligan has no fear of nude scenes, appearing with Michael Fassbender in the explicit film Shame and arguing that nakedness on screen has helped her overcome concerns about her body.

Carey Mulligan has stood by her decision to appear naked in dark sexual drama Shame. Photo/Supplied

"In my own life I'm very prudish about my body, or at least I have been in the past," Mulligan has said. "With respect to nudity, it was vital to the character in Shame, who wasn't supposed to be a very attractive character and needed to be emotionally naked and lost in different ways." Watson, alternatively, has been candid about a wish to protect her back catalogue, aware she will always be associated with the Harry Potter films. "I don't want everyone to forget me as Hermione. I am really proud of her," she has said.

The issue is not exclusively faced by young women. Justin Bieber supposedly recently refused to play a sex scene with another man in the film Uber Girl. Reports claimed he had demanded a rewrite of the script, although he has since denied this.

Romney suggests it can actually be more difficult for a male star to be taken seriously after a nude scene: "Because we're less used to seeing full frontal male nudity in mainstream cinema, it tends to be seen as anomalous, or comic," he said. "Viggo Mortensen's recent nude scene in Captain Fantastic is a bonus for his admirers, but it's also designed to elicit a kind of comic embarrassment because it's so unexpected."

Male nude scenes, such as Viggo Mortensen's recent one from Captain Fantastic, tend to damage the actor's career as well. Photo/Supplied.

Lina Esco, the actor and campaigner who founded the Free the Nipple movement after making a 2012 film about the taboo surrounding breasts, has a characteristically proactive approach. Publicising her uncompromisingly frank film, Fairy Dust, she told the New Musical Express she hopes to normalise female nudity rather than limit it.

"In the media," she said, "whenever you see a naked woman it's always sexualised, or to please someone else's eyes. I want to get to a place where women can be naked the same way that men can - funny naked or naked just to be naked."

Free the Nipple prostestors, like those in Auckland last year, hope to make the female body less scandalous. Photo / Doug Sherring

Attempts to reclaim the nude body for women, or to sanction justifiable sex scenes, remain difficult in such a male-dominated industry: the financiers, the director and the person pulling the focus on the camera are all likely to be men. "There's the old joke about the starlet who won't undress 'unless it's strictly integral to the plot' - and of course it somehow turns out to be always integral to the plot," Romney recalls.

At the same time, as he acknowledges, it would be a dimmer world without the surprising nudity involved in a scene such as the one in Robert Altman's Short Cuts in which Julianne Moore appears inexplicably naked from the waist down. Or, in contrast, the erotic charge of the scene in The Grifters in which Annette Bening's character runs naked down a corridor.

"It shows the character exulting in her awareness of her own sexual power - one of those rare moments when the cliches about nudity as empowerment take on some real meaning," he said.